An approach based on timed Petri nets and tree encoding to implement search algorithms for a class of scheduling problems

Scheduling problems have been approached several times by Petri nets. Indeed, the usage of a net model guarantees feasibility candidate solutions, but it does not provide an accurate evaluation time required to complete considered workshop. For this purpose, class timed nets, namely structured is defined and encoding structure information such nets as tree presented. This encoding, in combination with resolution some linear matrix inequalities, used estimate residual each job The main advantage computation estimation interval that includes necessarily exact duration. Consequently, lower bound never overestimates duration can be part cost function involved many exploration algorithms A* or Beam Search algorithms. In paper, proposed Hybrid Filtered algorithm performances are discussed for examples workshops. paper also illustrates approach combined supervisory control accelerate convergence since deadlocked solutions eliminated directly model.